We have
vector AB = (1 + 2)i + (2 - 3)j + (3 - 5)k = 3i - j - 2k
vector BC = (7 - 1)i + (0 - 2)j + (-1 - 3)k = 6i - 2j - 4k
vector CA = (7 + 2)i + (0 - 3)j + (-1 - 5)k = 9i - 3j - 6k
Now, |vector AB|2 = 14, |vector BC|2 = 56, |vector CA|2 = 126
⇒ |vector AB| = √14, |vector BC| = 2√14, |vector CA| = 3√14
⇒ |vector CA| = | vector AB| + |vector BC|
Hence the points A, B and C are collinear.